On '68's what I've seen is the chrome trim is attached to the base with a rectangular spring nut. Not shown in the FAM. The assembly is held to the body with Ford part 374566. Self threading Hex flange nut - 5/32" thread, .563" OD, 11/32" hex head, .290" thick w/sealer. AMK part WL, kit B-12974, 10 pcs. or kit F-3928, Quarter Panel ornaments.
'67 FAM calls out 372444 nuts, again self threading hex flange, 1/4" thread, 1.00" OD, 7/16" hex head, .375 thk w/sealer. AMK part OAA (similar), kit B-10641, 6 pcs (so you need 2 to get the 8 required). Or kit F-3947, Quarter panel ornaments.